Although most people have a rough idea of what Science Fiction is all about, there's not really a singular agreed on definition. Personally I'm a big fan of the one cooked up by Rod Serling's, The creator and host of the Twilight Zone. He once stated that; "Fantasy is the impossible made probable. Science Fiction is the improbable made possible." That being said, almost all big names in SF have their own idea of just what Science Fiction really is. You can check out Wikipedia's extensive list of SF definitions to get an idea of the variety of ideas out there.
"The best way to predict the future is to invent it." -Alan Kay
Did you know that the literally thousand year old Indian epic "Ramayana" (5th to 4th century before chirst) featured SF elements? Those ancient texts refer to flying contraptions that could traverse not just the skies but also space and the oceanic depths. These supremely speedy craft carried weapons of mass destruction so powerful that they could level entire cities! In the second century the Syrian-Greek writer Lucian wrote about a trip to space where he met alien life. In his conversation with them he criticized certain earthly behavior and in doing so Lucian became one of the first to employ SF as a tool for societal criticism He turned the lens back around, using it to look at ourselves through the eyes of an outsider. The first story that incorporated time travel as a device to study our ever more rapidly changing world emerged from Japan in the 8th century. In said story, a man who gets sent 300 years into the future desperately tries to find the way back to his old hometown in a for him almost unrecognizable world. It's clear that the history of SF goes back quite some time. From the mythic stories produced in ages nearly lost to history to the more recent European proto-SF movement and the 40s & 50s US golden age to ultimately the modern cyberpunk and biofunk of today. SF keeps renewing itself, a necessity brought about by its core task; to stay ahead of the future.
"Everything is becoming science fiction. From the margins of an almost invisible literature has sprung the intact reality of the 20th century." -J. G. Ballard
Science Fiction has a whole lot more to offer than just entertainment. SF can help us think through some of the possibly dangerous implications present in changing technology, culture or human nature. It allows us to simulate possible future scenarios which in a sense make it possible for us to anticipate and thus plan for and even guide our fates towards certain outcomes above others. There is a lively feedbackloop active between technological innovation and SF literature. Both push each other onward to ever greater feats of imagination and engineering prowess. A good example of this is the communication satellite which was first dreamt up by Arthur C. Clarke and took more then a decade to be translated from page to reality. Today more than 3000 of them circle or planet every day. People like Clarke allow us to pull a certain future into the present.
"A good science fiction story should be able to predict not the automobile but the traffic jam." -Frederik Pohl
"Politicians should read science fiction, not westerns and detective stories." -Arthur C. Clarke
The Encyclopedia of Science Fiction
Outline of Science Fiction - Wikipedia
Science Fiction Essentials
Science Fiction Classics
Forgotten Gems & Future Classics